Unparticle mediated superconductivity

In this work we introduce the possibility of unparticle mediated superconductivity. We discuss a theoretical scenario where it can emerge and show that a superconducting state is allowed by deriving and solving the gap equation for $s$-wave pairing of electrons interacting through the unparticle generalization of the Coulomb interaction. The dependence of the gap equation on the unparticle energy scale ${\mathrm{\Lambda }}_U$ and the unparticle scaling dimension $d_U$ enables us to find a richer set of solutions compared to those of the conventional BCS paradigm. We discuss unconventional features within this construction, including the resulting insensitivity of pairing to the density of states at the Fermi energy for $d_U=3\mathrm{/}2$ of the superconducting gap and suggest possible experimental scenarios for this mechanism.